Distance-estimation method for a travelling object subjected to dynamic path constraints

ABSTRACT

This method allows the calculation, using a terrain elevation database, of a map of the distances of the points accessible to a mobile object subjected to dynamic constraints evolving with its time of travel, for example an aircraft having an imposed vertical flight profile, the distances being measured solely according to paths achievable by the mobile object. It implements a propagation-based distance transform which catalogs the achievable paths going from a goal point whose distance is to be estimated to a source point which is the origin of the distance measurements and likens the distance of the goal point to the length of the shortest achievable path or paths.

The invention relates to terrain navigation in respect of a mobileobject subject to travel constraints varying over time, such as anaircraft limited in terms of rate of climb, the limit possibly beingnegative, and deploying above a terrain zone exhibiting threateningobstacles or reliefs close to or above its flight altitude.

Diverse systems have been developed for forewarning the crew of anaircraft of a risk of collision with the ground. Some, such as the TAWSsystems (the acronym standing for “Terrain Awareness and WarningSystem”), make a short-term trajectory forecast for the aircraft on thebasis of flight information (position, heading, orientation andamplitude of the speed vector) provided by the onboard equipment,situate this forecast with respect to a map of the region overflownextracted from a terrain elevation database accessible on board and emitalarms destined for the crew of the aircraft whenever the short-termforecastable trajectory comes into collision with the ground. These TAWSsystems supplement their alarms with rudimentary recommendations of thekind “Terrain Ahead, Pull up”. Some of them also give information aboutthe level of risk of collision incurred due to the reliefs and theobstacles surrounding the aircraft in the form of a map presenting thereliefs or the obstacles of the terrain overflown as strata of differentcolors. However, this map of risks of collision with the environmenttakes account only of the altitudes of the relief relative to theposition of the mobile object and does not take account of the existenceor otherwise of a realistic trajectory making it possible to join upwith the zones displayed.

To satisfy this requirement of ascertaining the points of the terrainoverflown that remain accessible after a maneuver for avoiding a reliefor an obstacle on the ground, the map of risk of collision with theenvironment must display only the zones for which there is a possibleroute from the current position of the mobile object. The realization ofsuch a display involves the association of a metric with a relief mapderived from a terrain elevation database.

A known procedure for associating a metric with a relief map derivedfrom a terrain elevation database with regular meshing of theterrestrial surface or of a part of the latter, consists in consideringthe map presenting the relief on the basis of altitude values appearing,with the geographical coordinates, latitude and longitude of themeasurement points, in the elements of the terrain elevation database asan image whose pixels are the altitude values of the points of theterrain elevation database that are illustrated in the map with, asabscissa and ordinate coordinates within the image, the latitude andlongitude geographical coordinates of these points appearing in theelements of the terrain elevation database and in calling upon adistance transform operating by propagation to estimate distances withinthis image.

Distance transforms operating by propagation also known as “chamferdistance transforms” or “chamfer Euclidean distance transforms” deducethe distance of a pixel termed the goal pixel with respect to anotherpixel termed the source pixel, from the distances previously estimatedfor the pixels of its neighborhood, through a scan of the pixels of theimage. The scan makes it possible to estimate the distance of a new goalpixel with respect to the source pixel by searching for the path ofminimum length going from the new goal pixel to the source pixel passingthrough an intermediate pixel of its neighborhood whose distance hasalready been estimated, the distance of the new goal pixel to anintermediate pixel of its neighborhood whose distance has already beenestimated being given by applying a neighborhood mask commonly called achamfer mask.

A distance transform of this kind was proposed in 1986 by GunillaBorgefors for estimating distances between objects in a digital image,in an article entitled: “Distance Transformation in Digital Images” andpublished in the journal “Computer Vision, Graphics and ImageProcessing”, Vol. 34 pp. 344-378. One of the interesting benefits ofthese propagation-based distance transforms is of reducing thecomplexity of the calculations of a distance estimate by permitting theuse of integers.

To select the path of minimum length giving the distance estimate, apropagation-based distance transform must test all the possible paths.This obligation is manifested as a regularity constraint imposed on theorder of scanning of the pixels of an image. G. Borgefors proposes, inorder to satisfy this regularity constraint, that the pixels of an imagebe scanned twice consecutively, in two mutually inverse orders, whichare either lexicographic order, the image being analyzed from left toright row by row and from top to bottom, and inverse lexicographicorder, or transposed lexicographic order, the image having undergone a90° rotation, and inverse transposed lexicographic order. She alsoproposes the adoption of a chamfer mask of dimensions 3×3 with twovalues (3, 4) of neighborhood distances or of dimensions 5×5 with threevalues (5, 7, 11) of neighborhood distances.

Distance transforms operating by propagation are already employed in thefield of terrain navigation for robots. In this context, it is known touse the distance transform of G. Borgefors with a static constraintconsisting in routinely allocating an infinite distance to a point underanalysis when it is apparent that it belongs to reliefs or obstacles tobe circumvented that are cataloged in a memory of prohibited crossingzones, so as to eliminate, from the set of the paths tested during adistance estimation, those passing through the reliefs or obstacles thatthe robot must circumvent. However, a distance transform operating bypropagation used with a static constraint within the context of terrainnavigation for robots, is not suitable for terrain navigation foraircraft for which the threat presented by a relief or an obstacle onthe ground depends on the vertical profile of its trajectory.

An aim of the present invention is a method of estimating the distancesof the points of a map extracted from a terrain elevation database withrespect to a reference point employing a distance transform operating bypropagation, with a dynamic constraint changing over, time suitable forterrain navigation for an aircraft having a trajectory with imposedvertical profile.

Its subject is a method of estimating the distances of the points of amap extracted from a terrain elevation database, for a mobile objectsubjected to dynamic constraints prohibiting it from certain zones ofthe map referred to as prohibited zones of passage whose configurationvaries as a function of the time of travel of the mobile object. Theterrain elevation database encompasses a set of points labeled by analtitude, a latitude and a longitude meshing the terrain of deploymentof the mobile object. The method implements a distance transformoperating by propagation over the image constituted by the elements ofthe terrain elevation database corresponding to the map and arranged inrows and columns in orders of values of longitude and latitude. Thisdistance transform estimates the distances of the various points of theimage with respect to a source point placed in proximity to the mobileobject, by applying, by scanning, a chamfer mask to the various pointsof the image. The estimation of distance of a point, by application ofthe chamfer mask to this point termed the goal point is performed bycataloging the various paths going from the goal point to the sourcepoint and passing through points of the neighborhood of the goal pointwhich are covered by the chamfer mask and whose distances from thesource point have been estimated previously in the course of the samescan, by determining the lengths of the various paths cataloged bysummation of the distance assigned to the point of passage of theneighborhood and of its distance from the goal point, extracted from thechamfer mask, by searching for the shortest path among the pathscataloged and by adopting its length as estimate of the distance of thegoal point. Initially, at the start of the scan, a distance valuegreater than the largest distance measurable on the image allocated toall the points of the image except for the source point, origin of thedistance measurements, to which is assigned a zero distance value. Themethod is noteworthy in that the lengths of the paths cataloged, duringthe application of the chamfer mask to a goal point, with a view tosearching for the shortest path, are translated into times of travel forthe mobile object and in that the cataloged paths whose times of travelfor the mobile object are such that the goal point would belong to aprohibited zone of passage at the moment at which the mobile objectreached it, are excluded from the search for the shortest path.

Advantageously, when the mobile object is an aircraft having a verticalflight profile to be complied with determining the evolution of itsinstantaneous altitude, there are associated, with the lengths of thecataloged paths, the forecastable values of the instantaneous altitudesthat the aircraft would have by reaching the goal point via these pathswhile complying with the vertical flight profile imposed, and thecataloged paths associated with forecastable values of altitude that areless than or equal to the goal point altitude given by the terrainelevation database and increased by a protection margin are eliminatedfrom the search for the shortest path.

Advantageously, when the mobile object is an aircraft having an imposedvertical flight profile, the distance estimation operated by propagationover the image constituted from the elements of the terrain elevationdatabase corresponding to the map is doubled up with an estimation ofthe forecastable altitude of the aircraft in line with the variouspoints of the image by assuming that it follows the shortest pathselected for the distance estimation and that it complies with thevertical flight profile imposed.

Advantageously, when the mobile object is an aircraft with imposedvertical flight profile and when the distance estimate is doubled upwith an estimate of the forecastable altitude of the aircraft, thealtitudes of the various points of the map are subtracted from theestimates of the forecastable altitudes of the aircraft at these pointsto obtain deviations with respect to the ground.

Advantageously, when the mobile object is an aircraft with imposedvertical flight profile and when the distance estimate is doubled upwith an estimate of the forecastable altitude of the aircraft, thealtitudes of the various points of the map are subtracted from theestimates of the forecastable altitudes of the aircraft at these pointsto obtain deviations with respect to the ground displayed on the map ascolor strata.

Advantageously, the propagation-based distance transform scans thepixels of the image constituted from the elements of the terrainelevation database corresponding to the map, in several successivepasses according to different orders.

Advantageously, the propagation-based distance transform scans thepixels of the image constituted from the elements of the terrainelevation database belonging to the map, in several successive passesaccording to different orders and repeatedly until the distanceestimates obtained stabilize.

Advantageously, the propagation-based distance transform scans thepixels of the image constituted from the elements of the terrainelevation database corresponding to the map, in several successivepasses according to different orders including lexicographic order,inverse lexicographic order, transposed lexicographic order and inversetransposed lexicographic order.

Advantageously, the propagation-based distance transform scans thepixels of the image constituted from the elements of the terrainelevation database corresponding to the map, in a series of four passesthat is repeated until stabilization of the distance estimates:

-   -   a first pass performed row by row from top to bottom of the        image, each row being traversed from left to right,    -   a second pass performed row by row from bottom to top of the        image, each row being traversed from right to left,    -   a third pass performed column by column from left to right of        the image, each column being traversed from top to bottom, and    -   a fourth pass performed column by column from right to left of        the image, each column being traversed from bottom to top.

Advantageously, the propagation-based distance transform scans thepixels of the image constituted from the elements of the terrainelevation database corresponding to the map, in a series of eight passesthat is repeated until stabilization of the distance estimates:

-   -   a first pass performed row by row from top to bottom of the        image, each row being traversed from left to right,    -   a second pass performed row by row from bottom to top of the        image, each row being traversed from right to left,    -   a third pass performed column by column from left to right of        the image, each column being traversed from top to bottom,    -   a fourth pass performed column by column from right to left of        the image, each column being traversed from bottom to top,    -   a fifth pass performed row by row from top to bottom of the        image, each row being traversed from right to left,    -   a sixth pass performed row by row from bottom to top of the        image, each row being traversed from left to right,    -   a seventh pass performed column by column from right to left of        the image, each column being traversed from top to bottom, and    -   an eighth pass performed column by column from left to right of        the image, each column being traversed from bottom to top.

Other characteristics and advantages of the invention will emerge fromthe description hereinbelow of an embodiment given by way of example.This description will be offered in conjunction with the drawing inwhich:

a FIG. 1 represents an exemplary chamfer mask,

FIGS. 2 a and 2 b show the cells of the chamfer mask illustrated in FIG.1, which are used in a scanning pass according to lexicographic orderand in a scanning pass according to inverse lexicographic order,

a FIG. 3 is a chart illustrating the main steps of a method, inaccordance with the invention, for estimating the distance of a pointhaving regard to a dynamic constraint in the course of the applicationof a chamfer mask,

a FIG. 4 is a chart illustrating a variant of the method of estimatingthe distance of a point shown in FIG. 3, and

a FIG. 5 is a chart of the main steps of a method, in accordance withthe invention, for estimating, by propagation, the distances of the setof the points of a map taking account of a dynamic constraint andimplementing a method of estimating the distance of a point such asthose shown in FIGS. 3 and 4.

The distance between two points of a surface is the minimum length ofall the possible routes over the surface starting from one of the pointsand finishing at the other. In an image formed of pixels distributedaccording to a regular mesh of rows, columns and diagonals, apropagation-based distance transform estimates the distance of a pixeltermed “goal” pixel with respect to a pixel termed “source” pixel byconstructing progressively, starting from the source pixel, the shortestpossible path following the mesh of pixels and finishing at the goalpixel, being aided by the distances found for the image pixels alreadyanalyzed and an array termed a chamfer mask cataloging the values of thedistances between a pixel and its close neighbors.

As shown in FIG. 1, a chamfer mask takes the form of an array with anarrangement of boxes reproducing the pattern of a pixel surrounded byits close neighbors. At the center of the pattern, a box assigned thevalue 0 labels the pixel taken as origin of the distances cataloged inthe array. Around this central box are clustered peripheral boxes filledwith non-zero distance values and mimicking the arrangement of thepixels of the neighborhood of a pixel assumed to occupy the central box.The distance value appearing in a peripheral box is that of the distanceseparating a pixel occupying the position of the peripheral boxconcerned, from a pixel occupying the position of the central box. It isnoted that the distance values are distributed as concentric circles. Afirst circle of four boxes corresponding to the four pixels closest tothe pixel of the central box that are placed either on the row or on thecolumn of the pixel of the central box are assigned a distance value D1.A second circle of four boxes corresponding to the four pixels closestto the pixel of the central box that are placed outside the row andcolumn of the pixel of the central box are assigned a distance value D2.A third circle of eight boxes corresponding to the eight pixels closestto the pixel of the central box that are placed outside the row, thecolumn and the diagonals of the pixel of the central box are assigned avalue D3.

The chamfer mask can cover a neighborhood of greater or lesser extent ofthe pixel of the central box by cataloging the values of the distancesof a greater or lesser number of concentric circles of pixels of theneighborhood. It may be reduced to the first two circles formed by thepixels of the neighborhood of a pixel occupying the central box or beextended beyond the first three circles formed by the pixels of theneighborhood of the pixel of the central box but it is customary to stopat first three circles like that represented in FIG. 1. The values ofthe distances D1, D2, D3 which correspond to Euclidian distances areexpressed in a scale permitting the use of integers at the cost of acertain approximation. Thus, G. Borgefors gives the value 5 to thedistance d1 corresponding to an echelon with abscissa x or with ordinatey, the value 7, which is an approximation of 5√{square root over (2)} tothe distance d2 corresponding to the root of the sum of the squares ofthe echelons with abscissa and ordinate √{square root over (x²+y²)}, andthe value 11, which is an approximation of 5√{square root over (5)}, tothe distance d3.

The progressive construction of the shortest possible path going to agoal pixel, starting from a source pixel and following the mesh ofpixels is done by regular scanning of the pixels of the image by meansof the chamfer mask. Initially, the pixels of the image are assigned aninfinite distance value, in fact a number high enough to exceed all thevalues of the distances measurable in the image, with the exception ofthe source pixel which is assigned a zero distance value. Then theinitial distance values assigned to the goal points are updated in thecourse of the scan of the image by the chamfer mask, an updateconsisting in replacing a distance value allocated to a goal point witha new lesser value resulting from a distance estimate made on theoccasion of a new application of the chamfer mask to the goal pointconsidered.

An estimation of distance by application of the chamfer mask to a goalpixel consists in cataloging all the paths going from this goal pixel tothe source pixel and passing through a pixel of the neighborhood of thegoal pixel whose distance has already been estimated in the course ofthe same scan, in searching from among the paths cataloged, for theshortest path or paths and in adopting the length of the shortest pathor paths as distance estimate. This is done by placing the goal pixelwhose distance it is desired to estimate in the central box of thechamfer mask, while selecting the peripheral boxes of the chamfer maskcorresponding to pixels of the neighborhood whose distance has just beenupdated, while calculating the lengths of the shortest paths connectingthe pixel to be updated to the source pixel while passing through one ofthe selected pixels of the neighborhood, by addition of the distancevalue assigned to the pixel of the neighborhood concerned and of thedistance value given by the chamfer mask, and in adopting, as distanceestimate, the minimum of the path length values obtained and of the olddistance value assigned to the pixel undergoing analysis.

The order of scanning of the pixels of the image influences thereliability of the distance estimates and of their updates since thepaths taken into account depend thereon. In fact, it is subject to aregularity constraint which implies that if the pixels of the image arelabeled in lexicographic order (pixels ranked in row-by-row ascendingorder starting from the top of the image and progressing toward thebottom of the image, and from left to right within a row), and if apixel p has been analyzed before a pixel q then a pixel p+x must beanalyzed before the pixel q+x. The lexicographic order (scanning of thepixels of the image row-by-row from top to bottom, and within a row,from left to right), inverse lexicographic order (scanning of the pixelsof the image row-by-row from bottom to top and, within a row, from rightto left), transposed lexicographic order (scanning of the pixels of theimage column-by-column from left to right and, within a column, from topto bottom), inverse transposed lexicographic order (scanning of thepixels by columns from right to left and within a column from bottom totop) satisfy this regularity condition and more generally all scans inwhich the rows and columns, or the diagonals are scanned from right toleft or from left to right. G. Borgefors advocates a double scan of thepixels of the image, once in lexicographic order and another time ininverse lexicographic order.

FIG. 2 a shows, in the case of a scan pass in lexicographic order goingfrom the upper left corner to the lower right corner of the image, theboxes of the chamfer mask of FIG. 1 that are used to catalog the pathsgoing from a goal pixel placed on the central box (box indexed by 0) tothe source pixel, passing through a pixel of the neighborhood whosedistance has already formed the subject of an estimate in the course ofthe same scan. These boxes are eight in number, arranged in the upperleft part of the chamfer mask. There are therefore eight paths catalogedfor the search for the shortest whose length is taken as estimate of thedistance.

FIG. 2 b shows, in the case of a scan pass in inverse lexicographicorder going from the lower right corner to the upper left corner of theimage, the boxes of the chamfer mask of FIG. 1 that are used to catalogthe paths going from a goal pixel placed on the central box (box indexedby 0) to the source pixel, passing through a pixel of the neighborhoodwhose distance has already formed the subject of an estimate in thecourse of the same scan. These boxes are complementary to those of FIG.2 a. They are also eight in number but arranged in the lower right partof the chamfer mask. There are therefore eight paths cataloged for thesearch for the shortest whose length is taken as estimate of thedistance.

The propagation-based distance transform whose principle has just beenrecalled briefly was designed originally for the analysis of thepositioning of objects in an image but it was soon applied to theestimation of the distances on a relief map extracted from a terrainelevation database with regular meshing of the terrestrial surface.Specifically, such a map is not furnished explicitly with a metric sinceit is plotted on the basis of the altitudes of the points of the mesh ofthe terrain elevation database of the zone represented. In this context,the propagation-based distance transform is applied to an image whosepixels are the elements of the terrain elevation database belonging tothe map, that is to say, altitude values associated with the latitude,longitude geographical coordinates of the nodes of the mesh where theyhave been measured, ranked, as on the map, by increasing or decreasinglatitude and longitude according to an array with two coordinatedimensions, latitude and longitude.

For terrain navigation of mobile objects such as robots, thepropagation-based distance transform is used to estimate the distancesof the points of the changing terrain map extracted from a database ofelevation of the terrain with respect to the position of the mobileobject or a close position. In this case, it is known to take account ofstatic constraints consisting of map zones that the mobile object cannotcross on account of their undulating configurations. Hence, aprohibited-zone marker is associated with the elements of the terrainelevation database appearing in the map. It signals, when it isactivated, an uncrossable or prohibited zone and blocks any updatingother than initialization, of the distance estimate made by thepropagation-based distance transform in respect of the pixel elementconsidered.

In the case of an aircraft, the uncrossable zones change as a functionof the vertical profile imposed on its trajectory so that a distanceestimate under static constraints by means of a propagation-baseddistance transform is not satisfactory.

It is proposed that account be taken, in the definition of theprohibited zones of passage, of the forecastable altitude of theaircraft at each goal point whose distance is currently being estimated.This forecastable altitude, which quite obviously depends on the pathfollowed, is that of the aircraft after negotiating the path adopted forthe distance measurement. The estimate of this forecastable altitude ofthe aircraft at a goal point is done by propagation in the course of thescan of the image by the chamfer mask in a manner similar to thedistance estimation. For each path cataloged going from a goal point tothe source point, passing through a point of the neighborhood of thegoal point, of which the distance to the source point and theforecastable altitude of the aircraft have already been estimated in thecourse of the same scan, the forecastable altitude of the aircraft isdeduced from the length of the path and the vertical profile imposed onthe trajectory of the aircraft. This forecastable altitude, estimatedfor each path cataloged going from a goal point whose distance iscurrently being estimated to a source point placed in proximity to theposition of the aircraft, is used as a criterion for selecting the pathstaken into account in the distance estimation. If it is less than orequal to the altitude of the goal point appearing in the terrainelevation database plus a safety margin, the cataloged path with whichit is associated is discarded and does not participate in the selectionof the shortest path. Once the selection of the shortest path has beenmade, its length is taken as distance of the goal point and theforecastable altitude of the aircraft which is associated therewith isalso retained as the altitude of the aircraft at the goal point.

FIG. 3 illustrates the main steps of the processing performed during theapplication of the chamfer mask to a goal point P_(i,j) to estimate itsdistance in respect of an aircraft having an imposed vertical trajectoryprofile. The goal point considered P_(i,j) is placed in the central boxof the chamfer mask. For each neighboring point P_(V) which enters theboxes of the chamfer mask and whose distance has already been estimatedin the course of the same scan, the processing consists in:

-   -   reading the estimated distance D_(V) of the neighboring point        P_(V) (step 30),    -   reading the altitude A_(i,j) of the goal point P_(i,j) in the        terrain elevation database (step 31),    -   reading the coefficient C_(XY) of the chamfer mask corresponding        to the box occupied by the neighboring point P_(V) (step 32),    -   calculating the propagated distance D_(P) corresponding to the        sum of the estimated distance D_(V) of the neighboring point        P_(V) and of the coefficient C_(XY) assigned to the chamfer mask        box occupied by the neighboring point P_(V):        D _(P) =D _(V) +C _(XY)        (step 33),    -   calculating the forecastable altitude A_(P) of the aircraft        after crossing of the distance D_(P) directly from the distance        D_(P) if the vertical profile imposed on the trajectory of the        aircraft is defined as a function of the distance traveled        PV(D_(P)) and takes implicitly into account the time of travel        or indirectly by way of the time of travel if the vertical        profile imposed on the trajectory of the aircraft is defined by        a rate of change of altitude (step 34),    -   comparing the forecastable altitude A_(P) obtained with that        A_(i,j) of the goal point P_(i,j) as derived from the terrain        elevation database increased by a safety margin Δ (step 35),    -   eliminating the propagated distance D_(P) if the forecastable        altitude A_(P) is less than or equal to that A_(i,j) of the goal        point P_(i,j) as derived from the terrain elevation database and        augmented by the safety margin Δ (step 36),    -   if the forecastable altitude A_(P) is greater than that A_(i,j)        of the goal point P_(i,j) augmented by the safety margin Δ,        reading the distance D_(i,j) already assigned to the goal point        considered P_(i,j) (step 37) and comparing it with the        propagated distance D_(P) (step 38),    -   eliminating the propagated distance D_(P) if it is greater than        or equal to the distance D_(i,j) already assigned to the goal        point considered P_(i,j) and    -   replacing the distance D_(i,j) already assigned to the goal        point considered P_(i,j) by the propagated distance D_(P) if the        latter is less (step 39).

FIG. 4 illustrates the main steps of a variant of the processingperformed during the application of the chamfer mask to a goal pointP_(i,j) to estimate its distance in respect of an aircraft having animposed vertical trajectory profile.

This variant differs in the manner of formulating the forecastablealtitude A_(P) of the aircraft. It assumes that the forecastablealtitude of the aircraft at each point of the terrain elevation databasecalculated as a function of the vertical profile imposed on itstrajectory and on the basis of the length of the path selected for thedistance measurement is not considered as a fleeting variable, therebyallowing the processing described in relation to FIG. 3, but is stored,in the same guise as the distance estimate. In this variant, steps 30,31 of reading the estimated distance D_(V) of the neighboring pointP_(V) and of the altitude A_(i,j) of the goal point P_(i,j) in theterrain elevation database are supplemented with a step 40 of readingthe forecastable altitude A_(PV) of the aircraft at the neighboringpoint P_(V), and the calculation of the forecastable altitude A_(P) isdone (step 34′) by summation of the forecastable altitude A_(PV) at theneighboring point P_(V) and of the variation of altitude over thedistance separating the neighboring point P_(V) from the goal pointP_(i,j) due to the vertical profile imposed on the trajectory of theaircraft.

The storage of the forecastable altitudes of the aircraft when thelatter reaches the various points of the map which are accessible by itmakes it possible to establish, by subtracting therefrom the altitudesof the points of the map as derived from the terrain elevation database,a map of the maximum possibilities of overfly heights of the aircraftrepresenting the forecastable deviations with respect to the terrain ascolor strata. Such a map helps the crew of the aircraft to choose arealistic trajectory exhibiting the best ground clearance.

As indicated previously, the estimation of the distances of the variouspoints of the map is done by applying a processing by chamfer mask suchas those just described in relation to FIGS. 3 and 4, to the whole setof pixels of the image formed by the elements of the terrain elevationdatabase belonging to the map, taken successively according to a regularscan comprising a minimum of two passes carried out in inverse orders.

FIG. 5 illustrates the main steps of an exemplary global processallowing the estimation of the distances of the set of points of arelief map for a mobile object subject to dynamic constraints.

The first step 50 of the process is an initialization of the distancesassigned to the various points of the map that are considered as thepixels of an image. This initialization of the distances consists, asindicated previously, in allocating an infinite distance value, at thevery least greater than the largest distance measurable on the map, forall the points of the map that are considered as goal points, with theexception of a single one considered as the source of all the distancesand to which a zero distance value is allocated. This source point ischosen in proximity to the instantaneous position of the mobile objecton the map.

The subsequent steps 51 to 54 are passes of a regular scan, in thecourse of which passes the chamfer mask is applied successively andrepeatedly to all the points of the map that are considered as thepixels of an image, the application of the chamfer mask to a point ofthe map giving an estimate of the distance of this point with respect tothe source point, by execution of one of the process operationsdescribed in relation to FIG. 3 or FIG. 4.

The first scan pass (step 51) is done in lexicographic order, the pixelsof the image being analyzed row by row from top to bottom of the imageand from left to right within one and the same row. The second scan pass(step 52) is done in inverse lexicographic order, the pixels of theimage still being analyzed row by row but from bottom to top of theimage and from right to left within a row. The third scan pass (step 53)is done in transposed lexicographic order, the pixels of the image beinganalyzed column by column from the left to the right of the image andfrom top to bottom within one and the same column. The fourth scan pass(step 54) is done in inverse transposed lexicographic order, the pixelsof the image being analyzed column by column but from right to left ofthe image and from bottom to top within one and the same column.

These four passes (steps 51 to 54) are repeated as long as the distanceimage obtained changes. To do this, the distance image content obtainedis stored (step 56) after each series of four passes (steps 51 to 54)and compared with the distance image content obtained in the previousseries (step 55), the loop being broken only when the comparison showsthat the content of the distance image no longer varies.

In theory, two scan passes in lexicographic order and inverselexicographic order may suffice. However, the presence of prohibitedzones of passage of concave shape may cause, in the distancespropagation phenomenon, dead angles enclosing pixels, for which theapplication of the chamfer mask does not give any distance estimate. Toreduce this risk of dead angle, it is advisable to vary the direction ofthe distance propagation phenomenon by varying the direction of thescan, hence the doubling of the passes with a transposition of theorders of scan corresponding to a 90° rotation of the image. For a yetbetter elimination of the dead angles, it is possible to undertakeseries of eight passes:

-   -   a first pass performed row by row from top to bottom of the        image, each row being traversed from left to right,    -   a second pass performed row by row from bottom to top of the        image, each row being traversed from right to left,    -   a third pass performed column by column from left to right of        the image, each column being traversed from top to bottom,    -   a fourth pass performed column by column from right to left of        the image, each column being traversed from bottom to top,    -   a fifth pass performed row by row from top to bottom of the        image, each row being traversed from right to left,    -   a sixth pass performed row by row from bottom to top of the        image, each row being traversed from left to right,    -   a seventh pass performed column by column from right to left of        the image, each column being traversed from top to bottom, and    -   an eighth pass performed column by column from left to right of        the image, each column being traversed from bottom to top.

It is possible to introduce into the series of scan passes other typesof scan passes deduced from the previous passes by making the diagonalsof the image play the roles previously played by the rows and columns ofthe image. This amounts to applying the scan passes described previouslyto an image rotated by 45°. In a general manner, the more the passes ofa series are varied the more the risk of dead angle decreases.

1. A method of estimating the distances of the points of a map extractedfrom a terrain elevation database, for a mobile object subjected todynamic constraints prohibiting it from certain zones of the mapreferred to as prohibited zones of passage whose configuration varies asa function of the time of travel of the mobile object; the terrainelevation database encompassing a set of points labeled by an altitude,a latitude and a longitude meshing the terrain of deployment of themobile object; said method implementing a distance transform operatingby propagation over the image constituted by the elements of the terrainelevation database corresponding to the map and arranged in rows andcolumns in orders of values of longitude and latitude; the distancetransform estimating the distances of the various points of the imagewith respect to a source point placed in proximity to the mobile object,by applying, by scanning, a chamfer mask to the various points of theimage; the estimation of distance of a point, by application of thechamfer mask to this point termed the goal point being performed bycataloging the various paths going from the goal point to the sourcepoint and passing through points of the neighborhood of the goal pointwhich are covered by the chamfer mask and whose distances from thesource point have been estimated previously in the course of the samescan, by determining the lengths of the various paths cataloged bysummation of the distance assigned to the point of passage of theneighborhood and of its distance from the goal point, extracted from thechamfer mask, by searching for the shortest path among the pathscataloged and by adopting its length as estimate of the distance of thegoal point; a distance value greater than the largest distancemeasurable on the image being initially allocated, at the start of thescan, to all the points of the image except to the source point, originof the distance measurements, to which is assigned a zero distancevalue; the said method being characterized in that the lengths of thepaths cataloged, during the application of the chamfer mask to a goalpoint, with a view to searching for the shortest path, are translatedinto times of travel for the mobile object and in that the catalogedpaths whose times of travel for the mobile object are such that the goalpoint would belong to a prohibited zone of passage at the moment atwhich the mobile object reached it, are excluded from the search for theshortest path.
 2. The method as claimed in claim 1, applied to anaircraft having a vertical flight profile to be complied withdetermining the evolution of its instantaneous altitude, wherein thelengths of the paths cataloged during the application of the chamfermask to a goal point, are associated the forecastable values of theinstantaneous altitudes that the aircraft would have by reaching thegoal point via these paths while complying with the vertical flightprofile imposed, and in that the cataloged paths associated withforecastable values of altitude that are less than or equal to the goalpoint altitude given by the terrain elevation database and increased bya protection margin are excluded from the search for the shortest path.3. The method as claimed in claim 2, wherein the distance estimationoperated by propagation over the image constituted from the elements ofthe terrain elevation database corresponding to the map is doubled upwith an estimation of the forecastable altitude of the aircraft in linewith the various points of the image by assuming that it follows theshortest path selected for the distance estimation and that it complieswith the vertical flight profile imposed.
 4. The method as claimed inclaim 3, wherein the altitudes of the various points of the map aresubtracted from the estimates of the forecastable altitudes of theaircraft at these points to obtain deviations with respect to theground.
 5. The method as claimed in claim 4, wherein the deviations withrespect to the ground are displayed on the map as color strata.
 6. Themethod as claimed in claim 1, wherein the propagation-based distancetransform scans the pixels of the image constituted from the elements ofthe terrain elevation database corresponding to the map, in severalsuccessive passes according to different orders.
 7. The method asclaimed in claim 6, wherein the propagation-based distance transformscans the pixels of the image constituted from the elements of theterrain elevation database corresponding to the map, in severalsuccessive passes according to different orders and repeatedly until thedistance estimates obtained stabilize.
 8. The method as claimed in claim6, wherein the propagation-based distance transform scans the pixels ofthe image constituted from the elements of the terrain elevationdatabase corresponding to the map, in several successive passesaccording to different orders including lexicographic order, inverselexicographic order, transposed lexicographic order and inversetransposed lexicographic order.
 9. The method as claimed in claim 6,wherein the propagation-based distance transform scans the pixels of theimage constituted from the elements of the terrain elevation databasecorresponding to the map, in a series of four passes that is repeateduntil stabilization of the distance estimates: a first pass performedrow by row from top to bottom of the image, each row being traversedfrom left to right, a second pass performed row by row from bottom totop of the image, each row being traversed from right to left, a thirdpass performed column by column from left to right of the image, eachcolumn being traversed from top to bottom, and a fourth pass performedcolumn by column from right to left of the image, each column beingtraversed from bottom to top.
 10. The method as claimed in claim 6,characterized in that wherein the propagation-based distance transformscans the pixels of the image constituted from the elements of theterrain elevation database corresponding to the map, in a series ofeight passes that is repeated until stabilization of the distanceestimates: a first pass performed row by row from top to bottom of theimage, each row being traversed from left to right, a second passperformed row by row from bottom to top of the image, each row beingtraversed from right to left, a third pass performed column by columnfrom left to right of the image, each column being traversed from top tobottom, a fourth pass performed column by column from right to left ofthe image, each column being traversed from bottom to top, a fifth passperformed row by row from top to bottom of the image, each row beingtraversed from right to left, a sixth pass performed row by row frombottom to top of the image, each row being traversed from left to right,a seventh pass performed column by column from right to left of theimage, each column being traversed from top to bottom, and an eighthpass performed column by column from left to right of the image, eachcolumn being traversed from bottom to top.
 11. The method as claimed inclaim 6, wherein the propagation-based distance transform scans thepixels of the image constituted from the elements of the terrainelevation database belonging to the map, in several successive passesaccording to different orders some of which consist of a scan of theimage by diagonals, from one edge to the other and, within a diagonal,from one end to the other.